Machine learning and privacy preserving algorithms for spatial and temporal sensing

Sensing physical and social environments are ubiquitous in modern mobile phones, IoT devices, and infrastructure-based settings. Information engraved in such data, especially the time and location attributes have unprecedented potential to characterize individual and crowd behaviour, natural and technological processes. However, it is challenging to extract abstract knowledge from the data due to its massive size, sequential structure, asynchronous operation, noisy characteristics, privacy concerns, and real time analysis requirements. Therefore, the primary goal of this thesis is to propose theoretically grounded and practically useful algorithms to learn from location and time stamps in sensor data. The proposed methods are inspired by tools from geometry, topology, and statistics. They leverage structures in the temporal and spatial data by probabilistically modeling noise, exploring topological structures embedded, and utilizing statistical structure to protect personal information and simultaneously learn aggregate information. Proposed algorithms are geared towards streaming and distributed operation for efficiency. The usefulness of the methods is argued using mathematical analysis and empirical experiments on real and artificial datasets

Constraints on quasi-normal-mode frequencies with LIGO-Virgo binary-black-hole observations

The no-hair conjecture in General Relativity (GR) states that a Kerr black hole (BH) is completely described by its mass and spin. As a consequence, the complex quasi-normal-mode (QNM) frequencies of a binary-black-hole (BBH) ringdown can be uniquely determined by the mass and spin of the remnant object. Conversely, measurement of the QNM frequencies could be an independent test of the no-hair conjecture. This paper extends to spinning BHs earlier work that proposed to test the no-hair conjecture by measuring the complex QNM frequencies of a BBH ringdown using parameterized inspiral-merger-ringdown waveforms in the effective-one-body formalism, thereby taking full advantage of the entire signal power and removing dependency on the predicted or estimated start time of the ringdown. Our method was used to analyze the properties of the merger remnants for BBHs observed by LIGO-Virgo in the first half of their third observing (O3a) run. After testing our method with GR and non-GR synthetic-signal injections in Gaussian noise, we analyze, for the first time, two BBHs from the first (O1) and second (O2) LIGO-Virgo observing runs, and two additional BBHs from the O3a run. We then provide joint constraints with published results from the O3a run. In the most agnostic and conservative scenario where we combine the information from different events using a hierarchical approach, we obtain, at $90\%$ credibility, that the fractional deviations in the frequency (damping time) of the dominant QNM are $\delta f_{220}=0.03^{+0.10}_{-0.09}$ ($\delta \tau_{220}=0.10^{+0.44}_{-0.39}$), respectively, an improvement of a factor of $\sim 4$ ($\sim 2$) over the results obtained with our model in the LIGO-Virgo publication. The single-event most-stringent constraint to date continues to be GW150914 for which we obtain $\delta f_{220}=0.05^{+0.11}_{-0.07}$ and $\delta \tau_{220}=0.07^{+0.26}_{-0.23}$.Comment: 15 pages, 8 figure

Constraining extra dimensions using observations of black hole quasi-normal modes

The presence of extra dimensions generically modify the spacetime geometry of a rotating black hole, by adding an additional hair, besides the mass $M$ and the angular momentum $J$, known as the `tidal charge' parameter, $\beta$. In a braneworld scenario with one extra spatial dimension, the extra dimension is expected to manifest itself through -- (a) negative values of $\beta$, and (b) modified gravitational perturbations. This in turn would affect the quasi-normal modes of rotating black holes. We numerically solve the perturbed gravitational field equations using the continued fractions method and determine the quasi-normal mode spectra for the braneworld black hole. We find that increasingly negative values of $\beta$ correspond to a diminishing imaginary part of the quasi-normal mode, or equivalently, an increasing damping time. Using the publicly available data of the properties of the remnant black hole in the gravitational wave signal GW150914, we check for consistency between the predicted values (for a given $\beta$) of the frequency and damping time of the least-damped $\ell=2,m=2$ quasi-normal mode and measurements of these quantities using other independent techniques. We find that it is highly unlikely for the tidal charge, $\beta \lesssim -0.05$, providing a conservative limit on the tidal charge parameter. Implications and future directions are discussed.Comment: 11 pages, 2 figures, 1 table, Revised version accepted in EPJ